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      Customer mobility and congestion in supermarkets

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          Abstract

          The analysis and characterization of human mobility using population-level mobility models is important for numerous applications, ranging from the estimation of commuter flows to modeling trade flows. However, almost all of these applications have focused on large spatial scales, typically from intra-city level to inter-country level. In this paper, we investigate population-level human mobility models on a much smaller spatial scale by using them to estimate customer mobility flow between supermarket zones. We use anonymized mobility data of customers in supermarkets to calibrate our models and apply variants of the gravity and intervening-opportunities models to fit this mobility flow and estimate the flow on unseen data. We find that a doubly-constrained gravity model and an extended radiation model (a variant of the intervening-opportunities model) can successfully estimate 65--70\% of the flow inside supermarkets. Using the gravity model as a case study, we then investigate how to reduce congestion in supermarkets using mobility models. We model each supermarket zone as a queue; and we use the gravity model to identify store layouts with low congestion, which we measure either by the maximum number of visits to a zone or by the total mean queue size. We then use a simulated-annealing algorithm to find store layouts with lower congestion than the original layout. In these optimized store layouts, popular zones are often in the perimeter of a store. Our research gives insight both into how customers move in supermarkets and into how retailers can arrange stores to reduce congestion. It also provides a case study of human mobility on small spatial scales.

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          A universal model for mobility and migration patterns.

          Introduced in its contemporary form in 1946 (ref. 1), but with roots that go back to the eighteenth century, the gravity law is the prevailing framework with which to predict population movement, cargo shipping volume and inter-city phone calls, as well as bilateral trade flows between nations. Despite its widespread use, it relies on adjustable parameters that vary from region to region and suffers from known analytic inconsistencies. Here we introduce a stochastic process capturing local mobility decisions that helps us analytically derive commuting and mobility fluxes that require as input only information on the population distribution. The resulting radiation model predicts mobility patterns in good agreement with mobility and transport patterns observed in a wide range of phenomena, from long-term migration patterns to communication volume between different regions. Given its parameter-free nature, the model can be applied in areas where we lack previous mobility measurements, significantly improving the predictive accuracy of most of the phenomena affected by mobility and transport processes.
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            The Gravity Equation in International Trade: Some Microeconomic Foundations and Empirical Evidence

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              A Proof for the Queuing Formula:L= λW

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                Author and article information

                Journal
                30 May 2019
                Article
                1905.13098
                2207e45b-d2ea-4f2c-8f0a-2f920dd43bd7

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                physics.soc-ph cs.SI

                Social & Information networks,General physics
                Social & Information networks, General physics

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